Enhance Learning Through Differentiated Instruction

The purpose of this webQuest is to present a model for differentiated instruction to classroom teachers who are  are unsure of how best to design and implement differentiated instruction within the mathematics classroom.

Effective instruction begins with differentiated instruction. There is strong research evidence that content differentiation is a very effective method for meeting students' educational need by providing each student with experiences and tasks that will expand and improve on his or her educational opportunities (Reis et al., 1992). Differentiated instruction promotes students’ deep conceptual understanding of content because the learning process occurs in the student's preferred learning style and at his or her ability level (DeJesus, 2012).  Differentiated instruction is not an instructional method as it is an approach to instruction that uses different instructional strategies that incorporate learning activities which  presents the content from an individual student's learning perspective that begins with his or her initial level of understanding of the content and focuses on the development and progress of that student's mastery of the content using his or her preferred learning style  (Watts-Taffeet al.. 2012).

There are a variety of approaches for differentiating tasks and each method can be the most effective when it meets the students' preferred method of learning and the teacher is able to design and deliver activities based on this method, i.e., the most effective task is that which is relatively  closest to the students' learning style and which the teacher is able to implement within the confines of classroom reality.

A differentiated instructional model of a calculus lesson is presented to demonstrate how instruction can be differentiated so as to meet all students' learning styles and educational needs.

Subject: Calculus (Mathematics)

Topic:  Maxima-Minima (New Lesson)

Objectives:

The students shall be able to:

1.         State the meaning of maxima-minima.

2.         Solve and locate the point where the maximum and minimum points of a

            given curve appears using the First Derivative Test (FDT).

Step 1- Students are given a written pre-test to assess their general knowledge of functions that includes graphs and evaluating zeros, critical values, minima and maxima to assess students’ readiness for mastering the concepts and skills necessary for this lesson.  

Step 2- The results of the pre-test will determine how the instruction will be planned.

a -  The students whose assessment results indicate that they lack the pre-requisite skills,   then these students will be my second level group and they will be grouped together for reviewing the required knowledge base of understanding and mastery of prerequisite skills of the lesson.

 b- The students with special needs will constitute the third level of differentiating the instructional plan. These are the students whose test results indicate that they have mastered the concepts or the students who require accommodations.  For those who have mastered the basic skills and concepts, they will be assigned enrichment activities such applications, in depth study, and computer based modeling. For students with special needs, one-on-one pull out tutoring sessions will be necessary initially to review the prerequisites necessary and introduce the new concepts. This part will be conducted by an   outside resource.

 

c- For the majority of the class the following activity will introduce the lesson’s concepts:

Students are placed in groups of three with similar learning style and mixed abilities. Each group is given a foot long piece of a wire, masking tape and a foot ruler. Students were asked to bend the wire to form a multi- peak arc. Students were then asked to use the masking tape and tape the wire in the note book such that at least one end point of the wire coincides with the longer side of a page in their note book and the entire wire is contained within that page. Students are asked to shape wire such that it represents the graph of what type of general relationship. Written instruction is provided that introduces the necessary vocabulary by drawing language structures from students via leading questions such as what would a concise scientific name would be for the peaks and the valleys, the highest peak lowest peak and the lowest valley.  

Procedure:

(1) The students will refine their definitions and share them with the class, until a mathematically acceptable definition has been arrived at.

(2) The instruction then asks the student to draw a tangent line at the peaks and the valleys and explore the value of the slope of these tangent lines and report what they have in common. Hopefully the students will realize that all these tangent lines will have a slope of zero.

(3) The instruction queries the students about the relationship between the slope of a line and the derivative. Then use that information to hypothesize about the derivative’s value at the maxima and the minima (peaks & valleys).  Hopefully the students will arrive at the hypothesis that the derivative’s value at the maxima and the minima is zero.

(4) Using leading questions in the form of Q & A, the groups are instructed to relate the sign of the slope of an increasing function, i.e., rising tangent lines, and decreasing functions, falling tangent lines. Then the groups are instructed to relate this observation to the derivative of the segment of the wire on either side of the maxima and the minima. The students hopefully will recognize that the signs are opposite.

Assessment:

The evaluation for level 3 groups will be based upon the activities assigned. They will be assessed on the concepts in the context of  assigned tasks.

Level 1 group will be assessed as follows:

(1) The teacher then asks the students to use the information obtained in step (4) to write out the wording of a hypothesis that pertains to the signs of the derivative of the function and the maxima/minima.   The students will refine their definitions and share them with the class. This process will be repeated until a mathematically acceptable definition of the FTD has been arrived at.

(2) The teacher then asks the classroom, given the rule of a function, how would you use calculus to arrive at the max and min points of that function? Hopefully the students will respond by saying, “Take the derivative of the function, set it to equal zero, and solve.” 

(3) The teacher asks, “How do you know what you have obtained in step (2) is a minimum or maximum point of the function?” and hopefully the students will respond, “by the order of the signs of the derivatives in either side of the maximum and minimum points. A (+, 0,-) indicates a maximum point, while a (-,0,+) indicates a maximum points.

Closure:

You have seen that if a point is maximum or minimum, then the derivative is zero. Is the converse true? Justify your answer.

Watts-Taffe et al. (2012) makes the following recommendations for teachers who are want to implement differentiated instruction methods in their classrooms:

a- Assess students on regular basis using different methods to determine patterns of need and group students accordingly.  

b- When selecting a differentiation strategy, modify the process, the materials, and product to suit the classroom’s reality, culture, and need.

c- Follow a gradual release of responsibility model in teaching as students begin to own responsibility of their own learning.

Using differentiated instruction methods different materials, classroom arrangement, and strategies are adapted to meet students’ readiness levels, interests and learning profiles. It is a recipe for classrooms where all students are included and can be successful. To accomplish this goal, a teacher establishes different expectations for students’ task completion based upon their individual needs.  To accomplish this goal, there teacher designs multiple levels for learning a lesson’s objectives. At the first level, instruction involves efforts to teach an entire class in the most effective ways such as group learning activities, visual demonstrations, modeling, etc. At the second leve, perhaps additional time or materials is provided for the relatively small number of students who do not learn from level 1methods. At third level, special cases at either exterme of the learning spectrum are provided with learning opportunities that meet their needs through entichment activities or individual tutoring outside of the classroom, depending on the case.

References

 

De Jesus, O. (2012). Differentiated Instruction: Can Differentiated Instruction Provide Success   for All Learners? National Teacher Education Journal, 5(3), 5-11.

 

Reis, S., Renzulli, J. (1992). Curriculum compacting: the complete guide to modifying the regular curriculum for high ability students. Mansfield Center, CT: Creative Learning Press.

 

Watts-Taffe, S., Laster, B., Broach, L., Marinak, B., McDonald Connor, C., & Walker-Dalhouse, D. (2012). Differentiated Instruction: Making Informed Teacher Decisions. Reading   Teacher, 66(4), 303-314.

References

 

De Jesus, O. (2012). Differentiated Instruction: Can Differentiated Instruction Provide Success   for All Learners? National Teacher Education Journal, 5(3), 5-11.

 

Reis, S., Renzulli, J. (1992). Curriculum compacting: the complete guide to modifying the regular curriculum for high ability students. Mansfield Center, CT: Creative Learning Press.

 

Watts-Taffe, S., Laster, B., Broach, L., Marinak, B., McDonald Connor, C., & Walker-Dalhouse, D. (2012). Differentiated Instruction: Making Informed Teacher Decisions. Reading   Teacher, 66(4), 303-314.